{
 "cells": [
  {
   "cell_type": "code",
   "id": "initial_id",
   "metadata": {
    "collapsed": true,
    "ExecuteTime": {
     "end_time": "2025-11-11T05:45:54.426915Z",
     "start_time": "2025-11-11T05:45:54.422922Z"
    }
   },
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ],
   "outputs": [],
   "execution_count": 11
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-11T05:45:54.450314Z",
     "start_time": "2025-11-11T05:45:54.445753Z"
    }
   },
   "cell_type": "code",
   "source": [
    "from numpy import log2\n",
    "\n",
    "p = np.arange(0.01, 1, 0.01)\n",
    "H = -p * log2(p) - (1 - p) * log2(1 - p)"
   ],
   "id": "9e484ff6c505ae8",
   "outputs": [],
   "execution_count": 12
  },
  {
   "metadata": {
    "ExecuteTime": {
     "end_time": "2025-11-11T05:45:54.542175Z",
     "start_time": "2025-11-11T05:45:54.463130Z"
    }
   },
   "cell_type": "code",
   "source": [
    "plt.plot(p, H)\n",
    "plt.show()"
   ],
   "id": "2b7f97933a01cc97",
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ],
      "image/png": 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"
     },
     "metadata": {},
     "output_type": "display_data",
     "jetTransient": {
      "display_id": null
     }
    }
   ],
   "execution_count": 13
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
